<description/> <author>Andrei Tokmakoff</author> <company/> <keywords/> <revisedBy>Andrei Tokmakoff</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>23B3F02E-DFE2-41C4-A1B7-46252D8FFF34</documentID> <versionID>E6826A49-C16F-4202-8689-D4917A864EDC</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> 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<currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="117" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="86" left="24" top="12.75" width="382.5" height="26.25" align-x="24" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Absorption Lineshape for the Displaced Harmonic Oscillator Model </inlineAttr> </f> <tab/>Finite temperature calculations </text> </region> <region region-id="85" left="24" top="50.25" width="90" height="12" align-x="24" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lets work in units of </text> </region> <region region-id="65" left="126" top="51" width="24.75" height="12.75" align-x="138" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="67" left="174" top="51" width="38.25" height="12.75" align-x="199.5" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">hbar</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="84" left="24" top="86.25" width="207" height="36" align-x="24" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Define the frequency of the electronic transition: <tab/> <tab/> <sp count="3"/>and the vibrational frequency: </text> </region> <region region-id="71" left="240" top="87" width="35.25" height="15" align-x="258" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">Ω</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="72" left="300" top="87" width="39.75" height="15" align-x="320.25" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> <ml:id xml:space="preserve" subscript="0">Ω</ml:id> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="74" left="240" top="111" width="30" height="15" align-x="257.25" align-y="120" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="83" left="24" top="140.25" width="239.25" height="12" align-x="24" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> The unitless displacement of the two harmonic wells is: </text> </region> <region region-id="117" left="276" top="141" width="33" height="12.75" align-x="289.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="82" left="24" top="170.25" width="139.5" height="12" align-x="24" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Define thermal occupation factor </text> </region> <region region-id="81" left="186" top="162" width="132" height="36" align-x="211.5" align-y="186" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">n</ml:id> <ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">hbar</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="88" left="48" top="207" width="86.25" height="12.75" align-x="72" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">g</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">g</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="95" left="24" top="236.25" width="95.25" height="12" align-x="24" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Set up frequency grid: </text> </region> <region region-id="94" left="150" top="237" width="42.75" height="12.75" align-x="159" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>100</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="93" left="228" top="237" width="85.5" height="18" align-x="243.75" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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Envelope of vibronic progression: </text> </region> <region region-id="55" left="30" top="378" width="264" height="44.25" align-x="78" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Env</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">n</ml:id> 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Lineshape for the Displaced Harmonic Oscillator Model </inlineAttr> </f> <tab/>Finite temperature calculations </text> </region> <region region-id="85" left="24" top="50.25" width="90" height="12" align-x="24" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lets work in units of </text> </region> <region region-id="65" left="126" top="51" width="24.75" height="12.75" align-x="138" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="67" left="174" top="51" width="38.25" height="12.75" align-x="199.5" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">hbar</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="84" left="24" top="86.25" width="207" height="36" align-x="24" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Define the frequency of the electronic transition: <tab/> <tab/> <sp count="3"/>and the vibrational frequency: </text> </region> <region region-id="71" left="240" top="87" width="35.25" height="15" align-x="258" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">Ω</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="72" left="300" top="87" width="39.75" height="15" align-x="320.25" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> <ml:id xml:space="preserve" subscript="0">Ω</ml:id> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="74" left="240" top="111" width="30" height="15" align-x="257.25" align-y="120" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="83" left="24" top="140.25" width="239.25" height="12" align-x="24" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> The unitless displacement of the two harmonic wells is: </text> </region> <region region-id="117" left="276" top="141" width="33" height="12.75" align-x="289.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="82" left="24" top="170.25" width="139.5" height="12" align-x="24" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Define thermal occupation factor </text> </region> <region region-id="81" left="186" top="162" width="132" height="36" align-x="211.5" align-y="186" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">n</ml:id> <ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">hbar</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="88" left="48" top="207" width="86.25" height="12.75" align-x="72" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">g</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">g</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="95" left="24" top="236.25" width="95.25" height="12" align-x="24" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Set up frequency grid: </text> </region> <region region-id="94" left="150" top="237" width="42.75" height="12.75" align-x="159" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>100</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="93" left="228" top="237" width="85.5" height="18" align-x="243.75" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>-5</ml:real> <ml:id xml:space="preserve" subscript="0">Ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="97" left="24" top="272.25" width="93.75" height="12" align-x="24" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Absorption lineshape: </text> </region> <region region-id="27" left="30" top="289.5" width="396" height="43.5" align-x="67.5" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">σ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">J</ml:id> </ml:boundVars> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">K</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:factorial/> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:real>10</ml:real> </ml:bounds> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:real>10</ml:real> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="99" left="24" top="350.25" width="141" height="12" align-x="24" align-y="360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Envelope of vibronic progression: </text> </region> <region region-id="55" left="30" top="378" width="264" height="44.25" align-x="78" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Env</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="103" left="0" top="438" width="6000" height="6" align-x="0" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="102" left="24" top="452.25" width="473.25" height="12" align-x="24" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Plot lineshapes for low, mid and high temperatures.<sp count="2"/>Temperature is defined relative to nuclear frequency (T/<f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">w)</inlineAttr> </f> </text> </region> <region region-id="31" left="60" top="483" width="12.75" height="12.75" align-x="65.25" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> </ml:parens> </math> <rendering item-idref="13"/> </region> <region region-id="32" left="84" top="483" width="36.75" height="12.75" align-x="96.75" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:real>0.01</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="33" left="132" top="474" width="35.25" height="30" align-x="150.75" align-y="492" 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> </ml:parens> </math> <rendering item-idref="18"/> </region> <region region-id="36" left="96" top="681" width="25.5" height="12.75" align-x="108.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="37" left="150" top="672" width="36.75" height="30" align-x="168.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="58" left="30" top="714" width="312.75" height="150" align-x="30" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="21"/> <rendering item-idref="22"/> </region> <region region-id="39" left="72" top="873" width="12.75" height="12.75" align-x="77.25" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> </ml:parens> </math> <rendering item-idref="23"/> </region> <region region-id="40" left="102" top="873" width="25.5" height="12.75" align-x="114.75" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="59" left="168" top="864" width="52.5" height="30" align-x="186.75" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.33333333333333331</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="60" left="54" top="912" width="312.75" height="150" align-x="54" align-y="912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="26"/> <rendering item-idref="27"/> </region> <region region-id="110" left="0" top="1080" width="6000" height="6" align-x="0" align-y="1080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="111" left="222" top="1149" width="36.75" height="12.75" align-x="234" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <result 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